Preconditioned numerical manifold method for linear elastic fractures

Fractures have attracted the attention of computational scientists for several decades. The modeling and simulation of fractures have been a major motivation for developing enriched finite element methods (FEMs), such as the numerical manifold method (NMM). However, ill-conditioning has always haunted NMM and other enriched FEMs when they are utilized for linear elastic fracture problems. Generally, ill-conditioning for a fracture problem is caused by two main issues: the arbitrary cut of the mesh by the fracture path and linear dependence related to the crack-tip enrichments. It is significantly challenging to overcome these two types of ill-conditioning using a single technique. In this study, we employ a preconditioner based on global normalization and local Gram-Schmidt orthogonalization of bases to eliminate these two ill-conditioning issues in NMM entirely and simultaneously. Various numerical examples have demonstrated that the proposed preconditioning strategy is highly effective in reducing the condition number and iteration counts of a iterative solver. It is highly robust, stable, and efficient and can be incorporated into enriched FEM programs to significantly facilitate the analyses of linear elastic fractures.(c) 2023 Elsevier B.V. All rights reserved.